Tosfos (Sanhedrin 74b DH v'Ha and elsewhere) posits that he does not. Normally, one must give his life rather than kill his fellow Jew, because "Why is your blood redder than the other's?" In the case of killing passively, though, the opposite argument aplies. "Why is his blood redder than yours ?"

The Rambam does not make a distinction between an active or passive killing. Rav Chaim Soloveitchik (Yesodei ha'Torah ch. 5) argues that it is impossible to "kill" passively. If a person allows himself to be thrown onto someone and squash the victim, the thrown party is simply a weapon , not a killer. The killer is the thrower.

The Chazon Ish argues (ibid.) that a person can kill passively by sitting on a person whose head is under the water and thereby causing him to drown, since such an act deems a person a killer according to the Gemara in Sanhedrin 76b.

Best wishes,

Mordecai Kornfeld